The lengths of my last 12 phone calls have been roughly 3, 8, 3, 5, 1, 13, 9, 2, 7, 3, 13, and 2 minutes. long experience suggests that the standard deviation is about 5 minutes.
a) i am asked what the average length of one of my phone calls is, and i shall estimate it by ; calculate this estimate and give its standard deviation (standard error).
b) assuming this is a large enough sample, write down a 98% confidence interval for the true value μ.

98% Confidence Interval: (2.387,9.113 )

Step-by-step explanation:

We are given the following data set:

3, 8, 3, 5, 1, 13, 9, 2, 7, 3, 13, 2

a) Formula:

where are data points, is the mean and n is the number of observations.  

Sum of squares of differences = 196.25

b) 98% Confidence Interval:

Putting the values, we get,  

step-by-step explanation:

subtract 7, so the answer is x < = 3, or c.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for